Information on Result #2175248
Linear OA(2257, 302, F2, 99) (dual of [302, 45, 100]-code), using adding a parity check bit based on linear OA(2256, 301, F2, 98) (dual of [301, 45, 99]-code), using
- construction XX applied to C1 = C([161,254]), C2 = C([169,4]), C3 = C1 + C2 = C([169,254]), and C∩ = C1 ∩ C2 = C([161,4]) [i] based on
- linear OA(2226, 255, F2, 94) (dual of [255, 29, 95]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−94,−93,…,−1}, and designed minimum distance d ≥ |I|+1 = 95 [i]
- linear OA(2219, 255, F2, 91) (dual of [255, 36, 92]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−86,−85,…,4}, and designed minimum distance d ≥ |I|+1 = 92 [i]
- linear OA(2235, 255, F2, 99) (dual of [255, 20, 100]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−94,−93,…,4}, and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(2210, 255, F2, 86) (dual of [255, 45, 87]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−86,−85,…,−1}, and designed minimum distance d ≥ |I|+1 = 87 [i]
- linear OA(216, 32, F2, 7) (dual of [32, 16, 8]-code), using
- Reed–Muller code RM(2,5) [i]
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2260, 305, F2, 99) (dual of [305, 45, 100]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2255, 300, F2, 97) (dual of [300, 45, 98]-code) | [i] | Truncation | |
| 3 | Linear OA(2254, 299, F2, 96) (dual of [299, 45, 97]-code) | [i] | ||
| 4 | Linear OOA(2257, 151, F2, 2, 99) (dual of [(151, 2), 45, 100]-NRT-code) | [i] | OOA Folding | |